kitchen table math, the sequel: fasten your seatbelts

Monday, September 24, 2007

fasten your seatbelts

I learned today that, last Thursday and Friday, C's math class -- this is Math A, algebra 1 & some geometry -- covered the following topics:

  • how to set up and solve algebra story problems in general

C. has never done any of these things, and, I am sad to say, was absent on Thursday and Friday when the kids did them in class.

So he missed out.

Teacher says it's not a problem. He can come in for extra help.



selected problems, 9-17-2007 thru homework 9-24-2007

  • During the first 6 months of last year, the interest on an investment was $130 less than during the second 6 months. The total interest for the year was $1,450. What was the interest for each 6-month period?
  • Find three consecutive integers such that twice the smallest is 12 more than the largest.
  • Saratoga and New York are 180 miles apart. A truck traveled from New York toward Saratoga at the rate of 65 miles per hour. Another truck traveled from Saratoga toward New York at the rate of 55 miles per hour. How many miles did each travel before they met?
  • (by + 2) / 3 = c, solve for y

Chris has no idea, none, how to do any of this stuff.

I know from experience that he will not learn how to do this stuff in Extra Help.



Susan J does homework

During the first 6 months of last year, the interest on an investment was $130 less than during the second 6 months. The total interest for the year was $1,450. What was the interest for each 6-month period?

This problem seems much complex that it is because of the mention of "6
months" and "interest on an investment" which has nothing to do with the
question. Here's the same problem with a different story.

The boss paid John and Fred $1450 total. John received $130 more than Fred.
How much did each receive?
Answer: John got $790 and Fred got $660.
[I think you could do this with a bar model.] [NOTE: That's exactly what I said! I have a note to myself to show C. how to do this problem using a bar model. - CJ]

On top of the other skills, have the students been taught how to determine irrelevant information? [My guess is that such a thing has never even been mentioned, but I don't absolutely know that for sure. I do know that if this subject did come up it was discussed briefly at most5.]


Find three consecutive integers such that twice the smallest is 12 more than the largest.

Here again, there is what you might call extraneous information or at least a two-part problem. The first part of the problem requires understanding what consecutive integers means and also how to solve two equations in two unknowns. Both are pretty sophisticated.

Let S be the smallest and L be the largest.
2S = L+12 (Twice the smallest is 12 more than the largest.)
L=S+2 (Consecutive integers are S, S+1, S+2, etc.)

2S = S+2+12 = S+14
S = 14

Answer: 14, 15, 16

Check 2 times 14 = 28; 28-12 = 16.
[Here I'd like to point out that C. has never, to my knowledge, been taught how to write "let x stand for _____" He has never been taught how to translate a simple algebra problem into an equation using unknowns. Never. Suddenly, he is supposed to be doing this. Or so I gather.]


Saratoga and New York are 180 miles apart. A truck traveled from New York toward Saratoga at the rate of 65 miles per hour. Another truck traveled from Saratoga toward New York at the rate of 55 miles per hour. How many miles did each travel before they met?

Are they supposed to know the distance = rate times time formula? [answer: I believe they covered it in class last Thursday or Friday. Before that he he wouldn't have known it, though he may have seen it before. - CJ]
Also, the problem does not explicitly state that they started at the same time so it requires some thought to realize that the times must be the same.

D1 = 65 * T1
D2 = 55 * T2
D1 + D2 = 180

Since T1 = T2 = T, we can substitute the first and second equations into the
third:
120 T = 180
T = 1.5

Check: 65 * 1.5 = 97.5
55 * 1.5 = 82.5

97.5 + 82.5 = 180

[C. has no idea how to set up a distance problem; nor does he know how to express one value in terms of another (e.g.. T1 = Ts). - CJ]


what my neighbor said

So I called up my neighbor to tell her C. had missed literal equations, distance problems, number problems, and general algebra story problems because he was out sick last Thursday and Friday, and, without missing a beat she said, "You need How to Solve Word Problems in Algebra. The section on number problems is really good."

"Yeah," I said. "It's supposed to be great. The Mildred Johnson book."

"Is it Mildred Johnson? How to solve algebra problems. That's the title."

"Yeah. It's Mildred Johnson. I have it on my desk."

"Oh, good. Use that."

This is an authentic Irvington school district conversation, mom to mom.

You call up your neighbor to tell her your kid missed out on literal equations, number problems, distance problems, and how to set up and solve a simple algebra problem and she says, "Use How to Solve Word Problems in Algebra."

This is why urban schools will never be high-performing.

How can urban schools be high-performing when urban moms have never even heard of How to Solve Word Problems in Algebra?*



*
presumably never heard of....

25 comments:

SteveH said...

I've never heard of literal equations, but I've done my share of solving for 'x, 'y', 'z', or whatever.

The problems are too much if this is their first exposure to converting words to equations, let alone solving the equations.

What book are they using for algebra and what pre-algebra book did they use last yeer. Pre-algebra is where students need to start learning how to set up and solve equations. I'll have to check my son's Glencoe Pre-Algebra book to see what it does.

Anonymous said...

I understand your frustration with how much C. missed in two days of absence. It sounds like there was a lot of content breezed over in those two days. These are enormously important topics, though. Geometry classes are chock full of angle and side-length problems that evolve into algebra problems.

For example: Two angles are supplementary; one is 10 more than two times the other. What are the measures of the angles.

This is a perfect application of "let x = angle A; let y = angle B. x + y = 180. x = 2y + 10.
Solve for y, then x.

Dan K.

Anonymous said...

http://www.regentsprep.org/Regents/math/formulas/litless.htm

Unknown said...

Catherine-
Although I'm not that familiar with the 5th & 6th grade Singapore curriculum, mainly because my kids "got" it and I didn't have to do much with them, I believe the number, number +1, number +2, equation is easily solved with a bar diagram. (At least, that's how I thought to solve it first)

As to the interest question, well, I agree with Susan J. That's why us problems are so annoying! Her less linguistically challenging (argh- interest!) John & Fred problem could be completed by my third graders. In fact, looks like a good problem for today!

Anonymous said...

The Mildred Johnson book is excellent. It's small and not expensive. It covers areas that the schools, once again, don't seem to be paying much attention to.

My son just worked straight from it without any help. The answers are detailed so that most kids will understand them if they miss the problem.

I with they had more books just like that.

Anonymous said...

I don't have a lisp. I "wish" they had more books like that.

Anonymous said...

When your district swiched over to the state math standards that came out in 2005, did the math dept. align the curriculum and make up gaps? Those two days seem to be review lessons for Math A given the current standards, but it's impossible to tell without knowing what the 6,7,&8th grade syllabi included at the time. Does the current teacher think it was a review ?

FWIW
Translate 2 step verbal expressions into algebraic notation is in 6th grade as standard 6.A.1 and in 7th - standard 7.A.1

8th is interesting, they are supposed to write verbal expressions to match given mathematical expressions, plus translate verbal sentences into inequalities (8.A.1, 8.A.2) as well as add and subtract polynomials with integer coefficients (8.A.8)

Solve and explain two step verbal expressions involving whole numbers using inverse operations was 6.A.4. and 7.A.4 covered the literal equations

Rate was in 6th - standard 6.N.6

The Math on Call reference book is handy on these. The test prep center that anon suggested is helpful too.

Anonymous said...

2 days absent = ineffective math instruction

Interesting equation.

PaulaV said...

"When your district swiched over to the state math standards that came out in 2005, did the math dept. align the curriculum and make up gaps?"

Last year I was told by my son's third grade teacher that the math curriuculm in my district did not align to our state standards. The teachers were upset about it, but there wasn't much they could do so they supplemented a great deal.

le radical galoisien said...

These are problems that naturally children should first spend months doing.

But doesn't the PSLE syllabus already deal with it?

The PSLE does algebra, without using letters.

So by the time you do use letters for the unknowns it's no big deal.

le radical galoisien said...

Besides, I've yet to encounter a problem within the algebra I and II syllabuses deal with Singapore's "changing ratios" problems.

LynnG said...

What curriculum are they using for this class?

Does the teacher just make it up as he goes along, or is there some method or plan to the random assignment?

I just can't imagine a teacher walking into an algebra 1 course for 8th graders and thinking four topics in 2 days was a brilliant way to achieve mastery.

Catherine Johnson said...

Hi Dan!!!

Great to see you!!!

Catherine Johnson said...

I've now heard back from the teacher (again) who says that he's teaching these topics over more than just two days....

Which is good.

That's not what he said in his first email, however.

In his first email, he said he'd taught these 4 topics in 2 days.

Anonymous said...

It is brilliant if the teacher also tutors....

Catherine Johnson said...

oh gosh --- must go get some other stuff done --- back in a bit

Cassy absolutely, BAR MODELS

Susan J said the same thing.

I'm going to see if I can have him do bar models for all of the "packet problems."

The difficulty, for the time being, seems to be that he is Xeroxing "packet problems" from the old AMSCO Math A book (which I have, along with the answer manual, fortunately).

That's fine -- I actually like the problems -- except that this is absolutely brand-new never-before-seen material for C.

Basically, the entire math curriculum in this district is a blo** mess.

That's just all there is to it.

AND the math department has a cavalier, even flippant attitude, to put it mildly.

Everyone knows the parents will hire tutors and the scores will be high.

Bottom line.

Catherine Johnson said...

Steve

They've just switched to Glencoe Algebra; they used Prentice Hall Pre-algebra in 6th grade; last year they AMSCO Integrated Math (not sure what that book is --- it's been chopped up and reassembled a number of times over the years).

Absolutely, they should have been setting up equations last year.

Catherine Johnson said...

I've mentioned several times that Ms. K didn't teach word problems.

What she did (I know I said this a few times) was put word problems on tests.

She used word problems as assessment tools; she didn't see word problems as content to be taught.

Catherine Johnson said...

The whole thing has been a nightmare.

As I believe you've noticed.

Catherine Johnson said...

Those two days seem to be review lessons for Math A given the current standards, but it's impossible to tell without knowing what the 6,7,&8th grade syllabi included at the time. Does the current teacher think it was a review ?

That was my question.

Ed assumes this was review....which would be normal at this time of year, right?

If it is review, the two-day time frame (which the teacher now says isn't two days, of course) would make more sense.

The problem is, no matter how you slice it, C. has never seen this material before, PERIOD. Which means most of the kids haven't seen it.

Even if the teacher is supposed to be doing review at this point (ideally) that's not where the kids are in the real world.

Catherine Johnson said...

Of course, in today's email he said C. was present for these lessons.....so.....

We may be entering uh-oh land.

Catherine Johnson said...

Nice to be home again!

Catherine Johnson said...

Test on Friday:

consecutive integers
motion
coins

He hasn't taught coin problems yet, C. says.

oh, well

This guy actually is a good teacher; I imagine his test will be on the material taught in class.

I'll teach to crammery over the next 3 days, and C. will end up with some sense of how to "Let x = ______"

I think he'll be able to do integer problems no sweat (I'm guessing); he'll be able to figure out coin problems.

Distance problems are tough.

Tough, tough, tough.

However, the teacher showed them how to do tables, which is a HUGE help.

I don't think C. has ever been taught to set up any kind of problem using a freaking table.

Catherine Johnson said...

I wonder if he remembers anything about percent?

Catherine Johnson said...

Must get back to cumulative practice.